NERS 312 Elements of Nuclear Engineering and Radiological Sciences II aka Nuclear Physics for ...

67 Pages·2016·3.74 MB·English

NERS 312
Elements of Nuclear Engineering and Radiological Sciences II
aka Nuclear Physics for Nuclear Engineers
Lecture Notes for Chapter 15: β decay
Supplement to (Krane II: Chapter 9)
The lecture number corresponds directly to the chapter number in the online book.
The section numbers, and equation numbers correspond directly to those in the online book.
c Alex F Bielajew 2012, Nuclear Engineering and Radiological Sciences, The University of Michigan
(cid:13)
A short illustrated story on the life of a neutron
from P. J. Fournier’s “What the Quark” website:
http://www.whatthequark.com/
devoted to “Cartoons about Life, Science, and What Not”.
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 2:15.0
Chapter 15: In this Chapter you will learn ......
Chapter 15.0: Basic introduction to β decay
The three views of β decay
•
Consequences of β-decay’s 3-body final state
•
Chapter 15.1: Energy release in β decay
Neutron decay
•
Q for β -decay
−
•
Q for β+-decay
•
Q for electron capture
•
Chapter 15.2: Fermi’s theory of β decay
Allowed transitions
•
Conventional forms: N0(p), N0(T )
e
•
Accounting of ”forbiddeness” and nuclear Coulomb effect.
•
The β-spectrum revealed
•
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 3:15.0
Chapter 15.3: Experimental tests of Fermi’s theory
Kurie plots: Shape of the β spectrum
•
Total decay rate: The ft , log ft values
1/2 10
•
Mass of the neutrino
•
Chapter 15.4: Angular momentum and parity selection rules
Classification of transitions in β decay
•
Examples of allowed β decays
•
Matrix elements for certain special cases
•
M = √2, for superallowed β decay’s
if
•
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 4:15.0
Chapter 15: β decay
β-particle’s are either electrons1 or positrons that are emitted through a certain class of
nuclear decay associated with the “weak interaction”.
The discoverer of electrons was Henri Becquerel, who noticed that photographic plates,
covered in black paper, stored near radioactive sources, became fogged.
The black paper (meant to keep the plates unexposed) was thick enough to stop α-
particles, and Becquerel concluded that fogging was caused by a new form of radiation,
one more penetrating than α-particles
The name “β”, followed naturally as the next letter in the Greek alphabet after α, α-
particles having already been discovered and named by Rutherford.
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 5:15.0
1Technically, the word “electron” can represent either a negatron (a fancy word for e−) or a positron (e+). I’ll use “electron”interchangeably with this meaning,and also
e−. Usually the context determines the meaning.
Since that discovery, we have learned that β-particles are about 100 times more penetrat-
1
ing than α-particles, and are spin- fermions.
2
Associated with the electrons is a conserved quantity, expressed as the quantum number
known as the lepton number.
The lepton number of the negatron is, by convention +1. The lepton number of the
positron, also the anti-particle2 of the negatron, is -1.
Thus, in a negatron-positron annihilation event, the next lepton number is zero. Only
leptons can carry lepton number. (More on this soon.) Recall, from Chapter 13 (Chapter
6 in Krane), our discussion of the various decay modes that are associated with β decay:
A A
X X + e + ν β decay
Z N Z+1 N′ 1 − e −
−→
−
A A + +
X X + e + ν β decay
Z N Z 1 N′ +1 e
−→
−
A A
X X + ν electron capture (ε) (1)
Z N Z 1 N′ +1 e
−→
−
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 6:15.0
2An anti-particle has the reverses signs of all the quantum numbers of its particle counterpart. When particle-particle annihilation occurs, all that remains is energy,
momentum, and angular momentum, as the sum of all quantum numbers must be zero.
We see from these processes that there are other particles called neutrinos.
1
Neutrinos are also spin- leptons (part of the larger fermion family). They are very nearly
2
massless (but proven to have mass3).
The electron neutrino is given the symbol ν , and has lepton number +1. The antineutrino,
e
the ν , has lepton number -1. A sketch of the organization of fundamental particles is
e
given in Figure 1.
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 7:15.0
3A direct measurement of neutrino mass suggests that its upper limit is mν <2.2eV. Indirect measurement of the neutrino mass suggest that 0.04eV< mν <0.3eV.
e e
For the more massive lepton family groups, mν <180keV, and mν <15.5MeV.
µ τ
Figure 1: The “Standard Model” classification of the fundamental particles.
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 8:15.0
Three views of β decay
There are three ways of viewing β decay.
The first is the “radiological physics view” expressed by (1).
The next is the “nuclear physics view”, where we recognize that the decays of the nuclei
are actually caused by transformations of the nucleon constituents, as expressed in (2).
n p + e + ν β decay
− e −
−→
+ +
p n + e + ν β decay
e
−→
p + e n + ν electron capture (ε) (2)
− e
−→
A free neutron will decay with a meanlife, τ = 885.7(8)s, about 11 minutes.
A free proton is basically stable. Once these nucleons are bound in a nucleus, however,
conservation of energy, with the availability of lower energy states, dictates whether or
not these processes are free to proceed.
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 9:15.0
Then, there is the more microscopic view, the “particle physics view” expressed in (3),
d u + e + ν β decay
− e −
−→
+ +
u d + e + ν β decay
e
−→
u + e d + ν electron capture (ε) (3)
− e
−→
that represents the transitions of nucleons, as really transitions between the up (u) and
down (d) quarks. A particle physics picture of β -decay is given in Figure 2.
−
Figure 2: The particle physics view of β -decay. In this case, the weak force is carried by the intermediate vector boson, the
−
+
W . In the case of β -decay, the weak force is carried by the intermediate vector boson, the W , the antiparticle to the
− −
0
W . There is also a neutral intermediate vector boson, Z , that is responsible for such things as νν scattering.
−
Nuclear Engineering and Radiological Sciences NERS 312: Lecture 15, Slide # 10:15.0